Toward discovering the excited <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math> baryons through nonleptonic weak decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>

Abstract

The nonleptonic weak decay processes ${\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Omega}}{\ensuremath{\pi}}^{+}/\mathrm{\ensuremath{\Omega}}(1P){\ensuremath{\pi}}^{+}/\mathrm{\ensuremath{\Omega}}(1D){\ensuremath{\pi}}^{+}/\mathrm{\ensuremath{\Omega}}(2S){\ensuremath{\pi}}^{+}$ are studied using the constituent quark model. The branching fraction of ${\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Omega}}{\ensuremath{\pi}}^{+}$ is predicted to be 1.05%. Considering the newly observed $\mathrm{\ensuremath{\Omega}}(2012)$ resonance as a conventional $1P$-wave $\mathrm{\ensuremath{\Omega}}$ excited state with spin parity ${J}^{P}=3/{2}^{\ensuremath{-}}$, the newly measured ratio $\mathcal{B}[{\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Omega}}(2012){\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}(\mathrm{\ensuremath{\Xi}}\overline{K}{)}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}]/\mathcal{B}[{\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Omega}}{\ensuremath{\pi}}^{+}]$ at Belle can be well understood. Besides, the production rates for the missing $1P$-wave state $\mathrm{\ensuremath{\Omega}}({1}^{2}{P}_{1/{2}^{\ensuremath{-}}})$, two spin quartet $1D$-wave states $\mathrm{\ensuremath{\Omega}}({1}^{4}{D}_{1/{2}^{+}})$ and $\mathrm{\ensuremath{\Omega}}({1}^{4}{D}_{3/{2}^{+}})$, and two $2S$-wave states $\mathrm{\ensuremath{\Omega}}({2}^{2}{S}_{1/{2}^{+}})$ and $\mathrm{\ensuremath{\Omega}}({2}^{4}{S}_{3/{2}^{+}})$ are also investigated. It is expected that these missing excited $\mathrm{\ensuremath{\Omega}}$ baryons should have large potentials to be discovered through the nonleptonic weak decays of ${\mathrm{\ensuremath{\Omega}}}_{c}$ in forthcoming experiments by Belle II and/or LHCb.

Topics & Concepts